Model 5  Split & Fraction Of Work Practice Questions Answers Test With Solutions & More Shortcuts

Question : 1 [SSC CGL Tier-II 2016]

A does $2/5$ of a work in 9 days. Then B joined him and they together completed the remaining work in 6 days. B alone can finish the whole work in

a) 8$2/11$ days

b) 6$12/13$ days

c) 18 days

d) 10 days

Answer: (c)

Remaining work = 1 - $2/5 = 3/5$ parts

(A + B) together do $3/5$th part of work in 6 days.

Time taken by A and B in doing whole work

= ${6 × 5}/3$ = 10 days

A does $2/5$th part of work in 9 days.

Time taken by A in doing whole work

= ${9 × 5}/2 = 45/2$ days

B’s 1 day’s work

= $1/10 - 2/45 = {9 - 4}/90 = 5/90 = 1/18$

Required time = 18 days

Question : 2 [SSC CHSL 2015]

If 12 men working 8 hours a day complete the work in 10 days, how long would 16 men working 7$1/2$ hours a day take to complete the same work?

a) 6

b) 7

c) 8

d) 10

Answer: (c)

Using Rule 1,

MenWorking hoursDays
12810
167$1/2$x

∴ ${16 : 12}/{15/2 : 8}]$ : : 10 : x

16 × $15/2$ × x = 12 × 8 × 10

8 × 15 × x = 12 × 8 × 10

$x = {12 × 8 × 10}/{8 × 15}$ = 8 days

Question : 3 [SSC CGL Tier-II 2015]

x does $1/4$ of a job in 6 days. y completes rest of the job in 12 days. Then x and y could complete the job together in

a) 9$3/5$ days

b) 9 days

c) 7$1/3$ days

d) 8$1/8$ days

Answer: (a)

Using Rule 2,

x does $1/4$ work in 6 days

x does 1 work in 24 days

Similarly,

y does $3/4$ work in12 days

y does 1 work in ${12 × 4}/3$ = 16 days

(x + y)’s 1 day’s work

= $1/24 + 1/16 = {2 + 3}/48 = 5/48$

Required time = $48/5 = 9{3}/5$ days

Question : 4 [SSC CHSL 2011]

A does half as much work as B in one-third of the time taken by B. If together they take 10 days to complete a work, then the time taken by B alone to do it would have been

a) 25 days

b) 30 days

c) 12 days

d) 6 days

Answer: (a)

Using Rule 2,

If B completes a work in x days,

A will complete the same in ${2x}/3$ days.

$1/x + 3/{2x} = 1/10$

${2 + 3}/{2x} = 1/10$

2x = 50 ⇒ x = 25 days

Question : 5 [SSC CHSL 2012]

A can do a work in 20 days and B in 40 days. If they work on it together for 5 days, then the fraction of the work that is left is :

a) $8/15$

b) $5/8$

c) $1/10$

d) $7/15$

Answer: (b)

Using Rule 2,

(A + B)’s 5 days’ work = $5(1/20 + 1/40)$

= $5({2 + 1}/40) = 15/40 = 3/8$

Remaining work = $1 - 3/8 = 5/8$

IMPORTANT QUANTITATIVE APTITUDE EXERCISES

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